vinay888 wrote:

A certain company sells jellybeans in the following six flavors only: b, c, g, l, p, s. If the jellybeans are sorted randomly into boxes containing exactly 2, 3, 4 different flavors only, what is the probability that any given box contain g jellybeans?

A 1/6

B 1/3

C 2/5

D 1/2

E 3/4

Can anyone please explain the answer?

First, I think it is easier to calculate the denominator first.

- Total outcomes in box with 2 different flavor : 6C2 = 15

- Total outcomes in box with 3 different flavor : 6C3 = 20

- Total outcomes in box with 4 different flavor : 6C4 = 15

- Total all possible outcomes = 50.Now, we can find the numerator.

- We can calculate probability of AT LEAST G in each boxes with : 1 - probability NO G in each boxes.

- Total outcomes WITHOUT G in box with 2 different flavor : 5C2 = 10

- Total outcomes WITHOUT G in box with 3 different flavor : 5C3 = 10

- Total outcomes WITHOUT G in box with 4 different flavor : 5C4 = 5

- Total outcomes WITHOUT G = 25, so total outcome AT LEAST G in each boxes = 50-25 = 25.Probability = \(\frac{25}{50}\) or \(\frac{1}{2}\).

Wdyt?

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